Time-frequency analysis of short segments of biomedical data

An evaluation is made of two novel methods in the tracking of variations in frequency of the various components present in an electroencephalogram (EEG) signal, for example when the subject is undergoing an epileptic seizure. In one method, the polynomial modelling method, the EEG is broken down into its constituent components using repeated polynomial modelling and zero crossing analysis is employed to characterise the time variation of the frequency of each component. In the second method, the phase compensation method, the signal is modelled as several cosines and the individual components are estimated and subtracted off the total signal; the phase derivative of each component is used to estimate the frequency. These methods are then compared with the conventional short time Fourier transform (STFT) and the high-order Yule-Walker (HOYW) methods. Using simulated data it is shown that the polynomial modelling method has the best performance in terms of breaking down the EEG into its constituent components. However, the HOYW and phase compensation methods provide estimates of the frequencies with lower variance. The three non-Fourier based methods are sensitive to the presence of noise and give similar estimates of the frequencies when applied to experimental non-pathological EEG data. The paper concludes with suggestions for combining the two novel methods to obtain a better frequency tracking performance.